Efficient sequential estimation in a markov branching process with immigration |
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Authors: | J.S. Jang D.S. Bai |
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Affiliation: | 1. Korea Advanced Institute of Science and Technology and Ajou University Suwon , Korea;2. Korea Advanced Institute of Science and Technology , POBox 150, Chongyangni Seoul, Korea |
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Abstract: | Sequential estimation of parameters In a continuous time Markov branching process with Immigration with split rate λ1 Immigration rate λ2, offspring distribution {p1j≥O) and Immigration distribution {p2j≥l} is considered. A sequential version of the Cramér-Rao type information inequality is derived which gives a lower bound on the variances of unbiased estimators for any function of these parameters. Attaining the lower bounds depends on whether the sampling plan or stopping rule S, the estimator f, and the parametric function g = E(f) are efficient. All efficient triples (S,f,g) are characterized; It Is shown that for i = 1,2, only linear combinations of λipij j's or their ratios are efficiently estimable. Applications to a Yule process, a linear birth and death process with immigration and an M/M/∞ queue are also considered |
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Keywords: | Markov branching process immignation information inequality closed sampling plan efficient estimation efficient triple |
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